Rhoticism

"Rhoticism" is a word occasionally encountered when one of the following is intended:

*Rhotacism, difficulty in pronouncing the /r/ sound
*Rhotacization, the articulation used to produce an r-colored vowel
*Rhoticity, the property that distinguishes rhotic and non-rhotic accents

According to the OED, "rhotacism" is NOT difficulty in pronouncing "r," but rather, the conversion of another sound (esp. s) into r. It can also be the excessive or peculiar use of "r," which might simply be, from the perspective of the non-rhotic British speakers responsible for the OED, any rhotic speech or use of the rolled "r."